Comment by credit_guy | Hacker News Reader

Comment by credit_guy | Hacker News Reader

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https://en.wikipedia.org/wiki/Isotopes_of_uranium

Natural uranium is a mix of 0.7% U-235 and 99.3% U-238. U-235 has a half-life of 700 million years and a spontaneous fission (SF) probability of 7e-11. U-238 has a half-life of 4.5 billion years and a SF probability of 5.4e-7. So on average it takes 6 times longer for a U-238 to decay than U-235, but when it does it has a probability to do it by spontaneous fission that is 7000 times higher. Add to that that U-238 is 141 times more plentiful in natural uranium, and you get that you can completely ignore U-235 when it comes to spontaneous fission.

1 kg of Uranium is about 4.2 moles. Each has 6e23 atoms (Avogadro's number), that's a total of about 25e23 atoms. Every year about 1 in 4.5 billion of those will decay one way or another. That's 5.5e14 decay events. The probability of spontaneous fission is 5.4e-7, so basically 10 million of these decay events are SF. There are 32 million seconds in a year, so I am getting about 0.3 SF events per second. On average a fission event generates about 2.5 neutrons, so that's close to 1 neutron per second.

They are getting 10 per second. They are nuclear engineers and I'm just a guy who knows how to multiply and how to read wikipedia. Most likely their number is correct.

> that's close to 1 neutron per second.

> They are getting 10 per second. They are nuclear engineers and I'm just a guy who knows how to multiply and how to read wikipedia. Most likely their number is correct.

Nicely done! It gets complicated, well beyond my current understanding. However, U238's first decay product is Thorium234, which has a half life of 24 days. Thorium234 in turn decays into Proactinium, which has a half life of 1.17 minutes. There are 16 more decays until finally arriving at Pb206 (lead), which is stable.

These decays must give room for lots more neutrons to emerge.

Those decays don't emit neutrons. Only spontaneous fissions make neutrons. The reactions you're talking about emit alpha particles, beta particles, and gamma rays.

If there are light element impurities in the uranium, or if the uranium is in a compound with light elements, there will be neutrons produced by (alpha,n) reactions on some of the light isotopes.

Some of the neutrons from spontaneous fission will hit other uranium atoms and cause non-spontaneous fission. Maybe enough to amplify it ten times?

Interesting. How much Uranium do we have on Earth?

For all practical purposes the quantity is infinite. The so-called "proven" reserves currently stand at 6 million tons [1]. But the quantity of uranium in seawater is staggering, of the order of 5 billion tons. It is estimated that, if needed, one could extract uranium from seawater at about 10 times the current cost of getting it from mines. That would add less than 1 cent to the price of 1 kWh of electricity generated by nuclear power plants. For comparison the average retail price of 1 kWh in the US is about 17 cents. Of course, nobody is seriously thinking of getting uranium from seawater because there are much cheaper ways to get it from mines. But any talk of uranium lasting only a few decades, or centuries is non-sense.

[1] https://world-nuclear.org/information-library/nuclear-fuel-c...

Depends on what you mean. If you mean "how much is commercially viable" versus "how many kilograms of the stuff are there" you get very, very different answers.

For just "how much stuff is there", we can look at the concentration in the earths crust, and we get about 10^17 kilograms of the stuff (10^15 if you want U-235).

If you just say "Sure, but we can't get most of that, how much can reasonably get extracted at current prices and technology" then you go down to about 10^9 kilograms.

The materials are also difficult to obtain without getting a rooftop guided Champagne delivery. Purchasing prepackaged materials is hard enough, making one is harder still.

Most of Earth's uranium is already engaged in commercially useful activity such as sustaining the geomagnetic field and the geological carbon cycle.

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